A new item response theory model for rater centrality using a hierarchical rater model approach

Abstract

Rater centrality, in which raters overuse middle scores for rating, is a common rater error which can affect test scores and subsequent decisions. Past studies on rater errors have focused on rater severity and inconsistency, neglecting rater centrality. This study proposes a new model within the hierarchical rater model framework to explicitly specify and directly estimate rater centrality in addition to rater severity and inconsistency. Simulations were conducted using the freeware JAGS to evaluate the parameter recovery of the new model and the consequences of ignoring rater centrality. The results revealed that the model had good parameter recovery with small bias, low root mean square errors, and high test score reliability, especially when a fully crossed linking design was used. Ignoring centrality yielded poor item difficulty estimates, person ability estimates, rater errors estimates, and underestimated reliability. We also showcase how the new model can be used, using an empirical example involving English essays in the Advanced Placement exam.

Identification of cheating methods in large-scale tests: Islamic education subject matter in the national examination

“…Outfit is based on the sum of squared standard residuals using conventional methods. Let X represent the observation, E denotes the expected value based on Rasch parameter estimation, and σ² represent the model's variance around its expectation (Qiu et al, 2021). The squared standard residual can then be calculated as: In this study, the researcher focused on three potential causes: cheating, careless mistakes, and lucky guessing.…”

A Bayesian many-facet Rasch model with Markov modeling for rater severity drift

“…The MFRM is the most common type of model used for IRT with rater parameters (Linacre, 1989 ). Furthermore, there are various alternative models such as a two-parameter logistic model with rater severity parameters (Patz & Junker, 1999 ), generalized partial credit models incorporating various rater parameters (Uto, 2021b ; Uto & Ueno, 2020 ), hierarchical rater models (DeCarlo, Kim, & Johnson, 2011 ; Patz, Junker, Johnson, & Mariano, 2002 ; Qiu, Chiu, Wang, & Chen, 2022 ), extensions based on signal detection models (DeCarlo, 2005 ; Soo Park & Xing, 2019 ), rater bundle models (Wilson & Hoskens, 2001 ), and trifactor models (Shin et al, 2019 ). However, this study focuses on the MFRM because it is the most widely used and well-established of these models.…”

“…Assuming data U , the proposed model defines the probability for as where d r m is a rater-specific step parameter denoting the severity for rater r of transitioning from score m − 1 to m , which is often used to examine the central tendency and the range restriction of each rater (Eckes, 2015 ; Myford & Wolfe, 2004 ; Qiu et al, 2022 ; Uto, 2021a ). Moreover, N ( μ , σ ) indicates a normal distribution of mean μ and standard deviation σ , and L N ( μ , σ ) indicates a log-normal distribution of mean μ and standard deviation σ on the log scale.…”